adaptivefence.fh {fence}

Adaptive Fence model selection (Small Area Estmation)

Description

Adaptive Fence model selection (Small Area Estmation)

Usage

adaptivefence.fh(mf, f, ms, d, lf, pf, bs, grid = 101, bandwidth, method)

Arguments

mf

Call function, for example: default calls: function(m, b) eblupFH(formula = m, vardir = D, data = b, method = "FH")

f

Full Model

ms

find candidate model, findsubmodel.fh(full)

d

Dimension number

lf

Measures lack of fit using function(res) -res$fit$goodness[1]

pf

Dimensions of model

bs

Bootstrap

grid

grid for c

bandwidth

bandwidth for kernel smooth function

method

Method to be used. Fay-Herriot method is the default.

Details

In Jiang et. al (2008), the adaptive c value is chosen from the highest peak in the p* vs. c plot. In Jiang et. al (2009), 95% CI is taken into account while choosing such an adaptive choice of c. In Thuan Nguyen et. al (2014), the adaptive c value is chosen from the first peak. This approach works better in the moderate sample size or weak signal situations. Empirically, the first peak becomes highest peak when sample size increases or signals become stronger

Value

models

list all model candidates in the model space

B

list the number of bootstrap samples that have been used

lack_of_fit_matrix

list a matrix of Qs for all model candidates (in columns). Each row is for each bootstrap sample

Qd_matrix

list a matrix of QM - QM.tilde for all model candidates. Each row is for each bootrap sample

bandwidth

list the value of bandwidth

model_mat

list a matrix of selected models at each c values in grid (in columns). Each row is for each bootstrap sample

freq_mat

list a matrix of coverage probabilities (frequency/smooth_frequency) of each selected models for a given c value (index)

c

list the adaptive choice of c value from which the parsimonious model is selected

sel_model

list the selected (parsimonious) model given the adaptive c value

Note

• The current Fence package focuses on variable selection. However, Fence methods can be used to select other parameters of interest, e.g., tunning parameter, variance-covariance structure, etc.

• The number of bootstrap samples is suggested to be increased, e.g., B=1000 when the sample size is small, or signals are weak

Author(s)

Jiming Jiang Jianyang Zhao J. Sunil Rao Thuan Nguyen

References

• Jiang J., Rao J.S., Gu Z., Nguyen T. (2008), Fence Methods for Mixed Model Selection. The Annals of Statistics, 36(4): 1669-1692

• Jiang J., Nguyen T., Rao J.S. (2009), A Simplified Adaptive Fence Procedure. Statistics and Probability Letters, 79, 625-629

• Thuan Nguyen, Jie Peng, Jiming Jiang (2014), Fence Methods for Backcross Experiments. Statistical Computation and Simulation, 84(3), 644-662

Examples

## Not run: 
require(fence)
### example 1 ####
data("kidney")
data = kidney[-which.max(kidney$x),]     # Delete a suspicious data point #
data$x2 = data$x^2
data$x3 = data$x^3
data$x4 = data$x^4
data$D = data$sqrt.D.^2
plot(data$y ~ data$x)
full = y~x+x2+x3+x4
testfh = fence.sae(full, data, B=1000, fence="adaptive", method="F-H", D = D)
testfh$sel_model
testfh$c

## End(Not run)